Revision notes for AQA GCSE Physics Resultant forces. Open the guide for explanations and worked examples. Written against the AQA GCSE Physics (8463) specification, so the content matches what's examinable rather than general Physics background.
Resultant forces
What you'll learn
- How forces are represented using arrows, with both size and direction.
- What a resultant force is, and how to calculate it for two forces in a straight line.
- How free-body diagrams show balanced and unbalanced forces.
- How Higher Tier scale vector diagrams can combine or split angled forces.
Forces: the starting point
A force is a push or a pull on an object. Forces are measured in newtons, symbol N.
A force can change an object’s speed, direction of motion, or shape. For this topic, the key idea is that a force has both a magnitude and a direction.
Definition
Magnitude
The magnitude of a force is its size. For example, a force of 20 N has a larger magnitude than a force of 5 N.
A quantity with both magnitude and direction is called a vector. Force is a vector quantity, so direction matters just as much as size.
When you draw a force, use an arrow:
- the arrow’s length represents the magnitude of the force
- the arrowhead shows the direction
- the label tells you the type and size of the force
Resultant force
Usually, more than one force acts on an object at the same time. Instead of thinking about every force separately, you can replace them with one single force that has the same overall effect.
Definition
Resultant force
The resultant force is the single force that has the same effect as all the forces acting on an object together.
Key Idea
Not an extra force
The resultant force is not an extra force added to the diagram. It is a replacement for the combined effect of the forces already acting.
If the resultant force is zero, the forces are balanced. If the resultant force is not zero, the forces are unbalanced.
Calculating resultants in a straight line
At GCSE, you must be able to calculate the resultant of two forces acting in the same straight line.
There are two cases:
- If the forces act in the same direction, add them.
- If the forces act in opposite directions, subtract the smaller force from the larger force.
The direction of the resultant is the direction of the larger force.
Example
Finding a resultant in a straight line
A box is pushed with 12 N to the right. Friction acts with 5 N to the left. Find the resultant force.
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The forces act in opposite directions, so subtract the smaller force from the larger force.
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Calculate the difference:
Fresultant=12 N−5 N=7 N\begin{aligned} F_\text{resultant} &= 12\ \text{N} - 5\ \text{N} \\ &= 7\ \text{N} \end{aligned}Fresultant=12 N−5 N=7 N -
The larger force acts to the right, so the resultant force is 7 N to the right.
Common Mistake
Forgetting the direction
A resultant force is a vector, so “7 N” is incomplete if direction matters. Write 7 N to the right, 8 N downward, or another clear direction.
Balanced and unbalanced forces
Balanced forces have a resultant force of zero. That means the object’s motion does not change.
This does not always mean the object is stationary. An object with balanced forces could be:
- stationary
- moving at a constant speed in a straight line
If the resultant force is not zero, the forces are unbalanced. The object’s motion changes: it may speed up, slow down, or change direction.
Key Idea
Zero resultant force
If the resultant force is zero, the forces are balanced and the object has no change in motion.
Example
Deciding whether forces are balanced
A crate has a weight of 100 N downward and a normal contact force of 100 N upward. It is pushed with 40 N to the right, and friction is 40 N to the left. Decide whether the forces are balanced.
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Compare the vertical forces: 100 N upward and 100 N downward are equal and opposite, so they cancel.
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Compare the horizontal forces: 40 N right and 40 N left are equal and opposite, so they cancel.
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There is no leftover force in any direction, so the resultant force is 0 N. The forces are balanced.
Common Mistake
Balanced does not mean stopped
Balanced forces mean no change in motion. A moving object can still have balanced forces if it continues at constant velocity.
Free-body diagrams
A free-body diagram is a simple diagram showing the forces acting on one chosen object. The object is often drawn as a box or dot, with force arrows drawn from it.
Definition
Free-body diagram
A free-body diagram shows all the forces acting on a single object, using labelled arrows to show their magnitudes and directions.
Free-body diagrams help you see which forces cancel and which forces produce a resultant.
Tip
Free-body diagram checklist
- Choose one object.
- Draw only the forces acting on that object.
- Label each force clearly, such as weight, friction, tension, air resistance, or normal contact force.
- Make larger forces look longer than smaller forces if the diagram is qualitative.
Example
Interpreting a free-body diagram
A lift has an upward tension force of 7000 N and a downward weight of 6500 N. Ignore air resistance. Find the resultant force and state whether the forces are balanced.
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The two forces act vertically in opposite directions, so subtract the smaller force from the larger force.
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Calculate the resultant:
Fresultant=7000 N−6500 N=500 N\begin{aligned} F_\text{resultant} &= 7000\ \text{N} - 6500\ \text{N} \\ &= 500\ \text{N} \end{aligned}Fresultant=7000 N−6500 N=500 N -
The larger force is upward, so the resultant force is 500 N upward. The forces are unbalanced.
Choosing the object or system
For Higher Tier, you also need to be comfortable describing forces on an isolated object or a system.
A system is the object or group of objects you choose to focus on. Forces between parts inside the system are called internal forces. Forces from outside the system are external forces.
For free-body diagrams, you usually show the external forces acting on the chosen object or system.
Example
Choosing a system
A car pulls a trailer along a road. Compare the forces you would consider if the system is just the trailer, or if the system is the car and trailer together.
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If the system is just the trailer, the pull from the car on the trailer is an external force, so it should be included.
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If the system is car plus trailer together, the pull between the car and trailer is internal to the system, so it is not shown as an external force on the whole system.
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For the car-plus-trailer system, you would still consider external forces such as driving force from the road, air resistance, weight, and normal contact forces.
Forces at angles: scale vector diagrams
This next part is Higher Tier only.
When forces do not act in the same straight line, you cannot just add their magnitudes. You need to take account of direction using a vector diagram.
A vector diagram is a scale drawing of vectors. For forces, each arrow represents a force with a chosen scale, such as 1 cm representing 1 N.
To find the resultant of two forces by scale drawing:
- Choose a sensible scale.
- Draw the first force with the correct length and direction.
- Draw the second force starting from the head of the first arrow.
- Draw the resultant from the start of the first arrow to the end of the second arrow.
- Measure the resultant’s length and direction.
Example
Finding a resultant by scale drawing
A force of 4 N acts east and a force of 3 N acts north. Use a scale drawing to find the resultant force.
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Choose a scale, such as 1 cm representing 1 N. Draw a 4 cm arrow east.
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From the head of that arrow, draw a 3 cm arrow north.
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Draw the resultant from the start of the 4 cm arrow to the end of the 3 cm arrow. Measure its length: it should be about 5 cm, so the resultant is about 5 N.
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Measure the angle from east using a protractor. The direction is about 37° north of east.
Tip
Equilibrium on a vector diagram
If force arrows placed head-to-tail form a closed shape, the resultant force is zero. That means the object is in equilibrium.
Resolving a force into components
This is also Higher Tier only.
Sometimes a single force acts at an angle. You can replace it with two forces at right angles to each other, usually one horizontal and one vertical. These are called components.
Definition
Component of a force
A component is one part of a force acting in a chosen direction. Two perpendicular components can have the same effect as the original angled force.
Resolving a force is the opposite of finding a resultant. Instead of combining two forces into one, you split one force into two perpendicular forces.
Example
Resolving a force using a scale drawing
A 10 N force acts at 30° above the horizontal. Estimate its horizontal and vertical components using a scale drawing.
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Choose a scale, such as 1 cm representing 2 N. Draw the 10 N force as a 5 cm arrow at 30° above the horizontal.
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Complete a right-angled triangle or rectangle so the diagonal is the original force, with one side horizontal and one side vertical.
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Measure the horizontal side. If it is about 4.3 cm, convert using the scale: 4.3 cm×2 N per cm≈8.6 N4.3\ \text{cm} \times 2\ \text{N per cm} \approx 8.6\ \text{N}4.3 cm×2 N per cm≈8.6 N.
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Measure the vertical side. If it is about 2.5 cm, convert using the scale: 2.5 cm×2 N per cm=5.0 N2.5\ \text{cm} \times 2\ \text{N per cm} = 5.0\ \text{N}2.5 cm×2 N per cm=5.0 N.
Common Mistake
Scale drawing accuracy
Your answer depends on drawing carefully. Use a sharp pencil, a sensible scale, and a protractor. Small drawing errors can change the measured resultant or components.
Exam technique
In the exam
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For forces in a straight line, decide whether they act in the same direction or opposite directions, then add or subtract and state the direction.
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For free-body diagrams, draw only the forces acting on the chosen object or system, not forces the object exerts on something else.
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For Higher Tier vector diagrams, use a clear scale, draw arrows head-to-tail, and measure both the magnitude and direction of the resultant.
Self review
Check yourself
- Two forces act on a trolley: 18 N left and 11 N right. What is the resultant force?
- A car moves at constant speed in a straight line. What can you say about the resultant force on it?
- Higher Tier: how would you use a scale drawing to find the resultant of 6 N north and 8 N east?
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